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A. Rs. 19200

B. Rs. 16000

C. Rs. 20000

D. Rs. 25000

Answer

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Let’s assume the market price to be Rs. $x$.

Since, it was on a discount of 40%.

We will use the formula:- Discount = \[\dfrac{{Discount\% }}{{100}} \times \] Market Price

We will now put in the given values.

So, we get:- Discount = $\dfrac{{40}}{{100}} \times x$

Simplifying the R.H.S, we get:-

Discount = $\dfrac{{4x}}{{10}}$

Now, we will use the formula:- Selling Price = S.P. = Market Price – Discount

So, we have, S.P. = $x - \dfrac{{4x}}{{10}}$.

Taking L.C.M. to simplify, we have:-

S.P. = $\dfrac{{10x - 4x}}{{10}} = \dfrac{{6x}}{{10}}$ …………(1)

We saw that the consumer bargained and got a further discount on S.P.

Discount further = 20%

We will now use the formula:- Further Discount = \[\dfrac{{Discount\% }}{{100}} \times \] S.P.

So, we get:- Further Discount = $\dfrac{{20}}{{100}} \times \dfrac{{6x}}{{10}}$

Simplifying the R.H.S,

Further Discount = $\dfrac{2}{{10}} \times \dfrac{{6x}}{{10}} = \dfrac{{12x}}{{100}}$ ……….(2)

Now, we will use the formula:- New S.P. = S.P. – Further Discount

Putting in the values we have using (1) and (2), we get:-

New S.P. = $\dfrac{{6x}}{{10}} - \dfrac{{12x}}{{100}}$

Taking L.C.M. to simplify, we have:-

New S.P. = $\dfrac{{60x - 12x}}{{100}} = \dfrac{{48x}}{{100}}$

Now, we will equate it to Rs. 9600 as we are given the final price in the question. SO we now have:-

$\dfrac{{48x}}{{100}} = 9600$

Taking 100 from denominator on L.H.S. to R.H.S.

$48x = 9600 \times 100 = 960000$

We can rewrite it as:-

$48x = 48 \times 20000$

Now, we will take 48 from L.H.S. to R.H.S.

$x = \dfrac{{48 \times 20000}}{{48}} = 20000$

Hence, the Market Price of the television is Rs. 20000.